Resonant-ring optical gyros rely on the frequency differences of resonant states in the ring between oppositely directed traveling electromagnetic waves resulting from the Sagnac effect to sense rotation rate. Empty or passive-ring gyros using mirrors exhibit lower performance because of the difficulty in suppressing unwanted higher-order transverse-mode resonances. Sagnac interferometer types of passive optical gyros use a coil of optical fiber instead of mirrors to develop a phase difference between the outputs of the clockwise and counterclockwise waves which is manifest as a shift in the interference pattern that varies with gyro rotation rate. But the Sagnac approach requires a long length of optical fiber and suffers from the presence of two orthogonal states of polarization, the difference in phase velocities of which is sensitive to environmental factors such as temperature, stress and magnetic fields. Also, to sense rotation, Sagnac gyros use an interference pattern phase shift detector with which it is more difficult to measure very small phase differences representative of small rates of rotation. Conventional passive resonant-ring optical gyros use two couplers--one coupler to simultaneously excite clockwise and counterclockwise traveling wave resonances and the other coupler to extract output signals representative of those waves. Two couplers require more precise and costly manufacturing to insure sensitivity of response in the clockwise and counterclockwise directions, and even then the excitation and reciprocity of opposite waves may not be identical. Dual couplers introduce more loss to the ring, thereby degrading its performance limit as a gyro. When both traveling wave resonances are excited in the resonant ring simultaneously, there will be interference from coherent backscattering and also from non-linear interactions due to the high electric field amplitudes at resonance that will be environmentally dependent, resulting in degrading gyro performance.